What is the vapor pressure in mmHg of a solution of 16.0 g of glucose (C6H12O6) in 80.0 g of methanol (CH3OH) at 27 degrees C? The vapor pressure of pure methanol at 27 degrees C is 140 mmHg.

Question

What is the vapor pressure in mmHg of a solution of 16.0 g of glucose (C6H12O6) in 80.0 g of methanol (CH3OH) at 27 degrees C?  The vapor pressure of pure methanol at 27 degrees C is 140 mmHg.

Ellie Andrews · Accepted Answer

#P_"sol" = "135 mmHg"#

In order to be able to determine the vapor pressure of this solution, you need to know two things

As you know, the vapor pressure of a solution that contains a non-volatile solute will depend exclusively on the mole fraction of the solvent, which in your case is methanol, and on the pure solvent's vapor pressure at that temperature

#color(blue)(P_"sol" = chi_"solvent" xx P_"solvent"^@)#

The mole fraction of the solvent will be equal to the number of moles of solvent divided by the total number of moles present in solution.

Use the molar masses of the two compounds to determine how many moles of each you have

#16.0 color(red)(cancel(color(black)("g"))) * ("1 mole C"_6"H"_12"O"_6)/(180.16color(red)(cancel(color(black)("g")))) = "0.08881 moles C"_6"H"_12"O"_6#

#80.0color(red)(cancel(color(black)("g"))) * ("1 mole CH"_3"OH")/(32.04color(red)(cancel(color(black)("g")))) = "2.4969 moles CH"_3"OH"#

The total number of moles present in solution will be

#n_"total" = n_"glucose" + n_"methanol"#

#n_"total" = 0.08881 + 2.4969 = "2.5857 moles"#

The mole fraction of methanol will be

#chi_"methanol" = (2.4969 color(red)(cancel(color(black)("moles"))))/(2.5857color(red)(cancel(color(black)("moles")))) = 0.9657#

The vapor pressure of the solution will thus be

#P_"sol" = 0.9657 * "140 mmHg" = "135.2 mmHg"#

I'll leave the answer rounded to three sig figs, despite the fact that you only have two sig figs for the vapor pressure of the pure solvent

#P_"sol" = color(green)("135 mmHg")#

Jeremiah Adams · Answer

undefined To find the vapor pressure of the solution, we first need to calculate the mole fraction of methanol and glucose in the solution. Then, we can use Raoult's law to find the vapor pressure of the solution.

Step 1: Calculate the moles of each component:
- Moles of glucose (C6H12O6):
   moles = mass / molar mass
   moles = 16.0 g / 180.16 g/mol = 0.0887 mol

- Moles of methanol (CH3OH):
   moles = mass / molar mass
   moles = 80.0 g / 32.04 g/mol = 2.497 mol

Step 2: Calculate the total moles of solute and solvent:
- Total moles = moles of glucose + moles of methanol
              = 0.0887 mol + 2.497 mol
              = 2.5867 mol

Step 3: Calculate the mole fraction of methanol:
- Mole fraction of methanol = moles of methanol / total moles
                             = 2.497 mol / 2.5867 mol
                             ≈ 0.9661

Step 4: Use Raoult's law to find the vapor pressure of the solution:
- Vapor pressure of the solution = mole fraction of methanol × vapor pressure of pure methanol
                                  = 0.9661 × 140 mmHg
                                  ≈ 135.254 mmHg

Therefore, the vapor pressure in mmHg of the solution is approximately 135.254 mmHg at 27 degrees C.